A major goal of superconductor research and development has been the discovery of useful substances that superconduct at the highest possible transition or critical temperatures Tc. Superconductivity can provide lossless flow of electrical current in a superconducting material as well as other beneficial physical characteristics.
The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity [see J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev., 108 (1957) 1175] ascribes the onset of the superconducting state of a crystal at the transition temperature Tc to electrons attractively paired via virtual phonons of the lattice. The BCS formula for Tc is:
                              T          c                =                              Θ            D                    ⁢                      exp            ⁡                          (                              -                                  1                                                            N                      ⁡                                              (                        0                        )                                                              ×                    V                                                              )                                                          (                  Eq          .                                          ⁢          1                )            where ΘD is the lattice Debye temperature, V is the attractive potential between electrons in Cooper pairs [see L. N. Cooper, Phys. Rev., 104 (1956) 1189] induced by the electron-phonon interactions, and N(0) is the electronic density of states for one spin at the Fermi energy.
The BCS theory together with its strong-coupling extension has been eminently successful in accounting for the physical properties, e.g., non-dissipative current, diamagnetism, and thermodynamics of the superconducting state of high-dimensional metals, and it has correlated many experimental data in terms of a few basic parameters. Nevertheless, it has often been emphasized that the BCS theory and formal extensions thereof do not satisfactorily explain the observed dependence of superconductivity on crystal structure and chemistry (especially for transition metals, alloys, and compounds) and are not very useful for predicting which materials should be superconducting and which should not. [See B. T. Matthias, Phys. Rev., 97 (1955) 74; in C. J. Gorter (ed.), Progress in Low Temperature Physics, Vol. II, North-Holland, Amsterdam, 1957, p. 138; in W. D. Gregory, W. N. Matthews, Jr. and E. A. Edelsack (eds.), The Science and Technology of Superconductivity, Vol. 1, Plenum, New York, 1973, p. 263; Physica, 55 (1971) 69.] Moreover, the BCS theory has failed to explain the origin and properties of high-Tc superconductivity in low-dimensional (e.g. “layered”) materials such as the cuprates [see J. G. Bednorz and K. A. Muller, Z. Phys. B64 (1986) 189] and recently discovered LaOFeAs superconductors [see Y. Kamihara et al., J Am. Chem. Soc. 130 (2008) 3296].
The existence of such high-Tc superconducting materials, having short “coherence lengths”, and those possessing only short-range structural order, such as superconducting amorphous alloys [see W. L. Johnson, S. J. Poon and P. Duwez, Phys. Rev., B11 (1975) 150] and super-conducting metal particles down to 50 Angstroms (Å) in size [see S. Matsuo, H. Sugiura and S, Noguchi, J Low-Temp. Phys., 15 (1974) 481; and K. Ohshima, T. Kuroshi and T. Fujita, J Phys. Soc. Jpn., 41 (1976)1234], would appear to be more conveniently viewed from a local “real-space” chemical approach, than by traditional concepts of long-range crystalline order and momentum (k) space, which lead to coherence lengths of the superconducting state that usually exceed the short-range order and electron mean free path characteristic of such superconductors. This emphasizes the desirability of having a local chemical-bonding or real-space molecular description of the superconducting state in order to complement BCS theory. Indeed, London [see F. London and H. London, Proc. R. Soc. London, Ser. A, 149 (1935) 71; Physica, 2 (1935) 341; F. London, Proc. R. Soc. London, Ser. A, 152 (1935) 24; and F. London, Superfluids, Vol. 1, Wiley, New York, 1950] in his phenomenological approach to superconductivity discusses the possibility of developing a molecular description of the superconducting state (see Chapter E of London's Superfluids), and Slater [see J. C. Slater, Phys. Rev., 51 (1937) 195; 52 (1937) 214] in an early attempt at describing superconductivity discusses the nature of the spatial character of the superconducting-state wave function. With speculations that mechanisms other than electron-phonon coupling can attractively pair electrons in the superconducting state [see W. A. Little, Phys. Rev., 134 (1964) A1416; H. Gutfreund and W. A. Little, in J. T. Devreese, R. P. Evrard and V. E. Van Doren (eds.), Highly Conducting One-Dimensional Solids, Plenum, New York, 1979, p. 305], a molecular criterion that accounts for the known chemical trends in the occurrence of superconductivity would be a useful tool in the ongoing effort to identify novel superconductors.